A298437 Numbers n such that there are precisely 16 groups of orders n and n + 1.

83132, 86049, 173529, 492830, 704241, 889406

Offset: 1

Author

Muniru A Asiru, Jan 19 2018

Keywords

• nonn
• more

Comments

Equivalently, lower member of consecutive terms of A295161.

Examples

			For n = 83132, A000001(83132) = A000001(83133) = 16.
For n = 173529, A000001(173529) = A000001(173530) = 16.
For n = 492830, A000001(492830) = A000001(492831) = 16.
		

Links

• H. U. Besche, B. Eick and E. A. O'Brien, A Millennium Project: Constructing Small Groups, Internat. J. Algebra and Computation, 12 (2002), 623-644.
• Gordon Royle, Numbers of Small Groups
• Index entries for sequences related to groups

Crossrefs

Cf. A000001. Subsequence of A295161 (Numbers n having precisely 16 groups of order n). Numbers n having precisely k groups of orders n and n+1: A295230 (k=2), A295990 (k=4), A295991 (k=5), A295992 (k=6), A295993 (k=8), A298427 (k=9), A298428 (k=10), A295994 (k=11), A298429 (k=12), A298430 (k=13), A298431 (k=14), A295995 (k=15), this sequence (k=16).

Programs

Maple

with(GroupTheory): for n from 1 to 10^6 do if [NumGroups(n), NumGroups(n+1)] = [16, 16] then print(n); fi; od;

Formula

Sequence is { n | A000001(n) = 16, A000001(n+1) = 16 }.